Anisotropic charge trapping in phototransistors unlocks ultrasensitive polarimetry for bionic navigation

Being able to probe the polarization states of light is crucial for applications from medical diagnostics and intelligent recognition to information encryption and bio-inspired navigation. Current state-of-the-art polarimeters based on anisotropic semiconductors enable direct linear dichroism photodetection without the need for bulky and complex external optics. However, their polarization sensitivity is restricted by the inherent optical anisotropy, leading to low dichroic ratios of typically smaller than ten. Here, we unveil an effective and general strategy to achieve more than 2,000-fold enhanced polarization sensitivity by exploiting an anisotropic charge trapping effect in organic phototransistors. The polarization-dependent trapping of photogenerated charge carriers provides an anisotropic photo-induced gate bias for current amplification, which has resulted in a record-high dichroic ratio of >104, reaching over the extinction ratios of commercial polarizers. These findings further enable the demonstration of an on-chip polarizer-free bionic celestial compass for skylight-based polarization navigation. Our results offer a fundamental design principle and an effective route for the development of next-generation highly polarization-sensitive optoelectronics.


I. Compact model of organic field-effect transistors
We utilized the compact model of organic field-effect transistors (OFETs) developed by Estrada et al. 1,2 to simulate the transfer characteristics of a phototransistor. The model can well explain the drain current (IDS) both in the above-threshold regime and the sub-threshold regime. The abovethreshold drain current (Iabove) of a p-type OFET can be described as the product of three parts: channel conductance (gch), effective drain voltage (VDSe) for a smooth linear-to-saturation transition, and a modified asymptotic expression [1+λs(|VDS|−αs|VG−Vth|)] for better describing the output conductance: where W and L are the channel width and length of the device, respectively, Ci is the unit-area capacitance of the dielectric layer, μFET is the field-effect mobility, VG is the gate voltage, Vth is the threshold voltage, VDS is the drain voltage, Rc is the contact resistance, m is the linear-to-saturation transition parameter, λs is the saturation coefficient, and αs is the saturation modulation parameter. For simplicity, we now consider an ideal case where Rc = 0, and a VG-independent intrinsic mobility of the active material (μin) is used instead of μFET. Iabove can thus be written as: The sub-threshold drain current (Isub) can be expressed as: where I0 is the off-state current, SS is the subthreshold swing, and Von is the onset voltage. A hyperbolic tangent transition function is used to combine the two regimes together. The total IDS is:  (Supplementary Fig. 1).

Supplementary Figure 1 | Model construction of an ideal OFET. Transfer characteristics of an ideal
OFET described by the compact model.

Supplementary
for E ⊥ we have: The threshold voltage difference between the two polarization states is thus: 9 in eff th,PD th, th, 9 eff 1 5.88 10 = = 19.94 ln 1 5.88 10 According to the above equation, as Peff increases, ΔVth,PD will gradually become saturated ( Supplementary Fig. 3a). Therefore, for a particular ain, we can estimate the upper limit of ΔVth,PD that can be obtained. E.g., for C8-BTBT crystals we used for fabricating OPTs in following discussions, the maximum ΔVth,PD is estimated to be ~34.2 V with ain = 5.6 ( Supplementary Fig. 3b). Since our estimations are based not on the absolute value of Vth but on the change in Vth under polarized light, the exact position of threshold/onset point in the dark does not impact our conclusions. Therefore, we utilize the compact model in Section I and assign the threshold/onset point of Ilight, ⊥ as reference zero.
The relative value of Ilight, ‖ can be attained with ΔVth,PD = ΔVon,PD = ΔVB,PD = 34.2 V, and further the ain-related DR can be predicted. Note that the subthreshold current I0 may be higher under light illumination due to the generation of excess charge carriers. Therefore, I0 is set to be 10 -9 A for a more accurate prediction in our case. The DR can reach over 10 4 in PV mode compared to the limited value (DR ≤ 5.6) in PC mode ( Supplementary Fig. 4a). Further, it is suggested that fabricating high-quality photoactive crystals with a larger μin is favorable for attaining a much higher DR ( Supplementary Fig.   4b).
Supplementary The relative VG represents the applied gate voltage relative to the reference onset/threshold point of Ilight, ⊥ .

IV. Optical anisotropy analyses of C8-BTBT
The optical absorption process in organic semiconductors is related to the excitation of charge carriers from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). According to the Davydov theory 11 , the anisotropic optical absorption of herringbonetype organic semiconductor crystals is attributed to the orientation difference of adjacent molecules 12,13 .
The resonant interaction between two differently oriented adjacent molecules will lead to the Davydov splitting of molecular terms. The Davydov components can be identified by the dimer energies of exciton states: where E0 and E * are the energies of ground and excited states, respectively, D' is the Coulomb interaction energy in the excited state, and I12 is the resonance interaction energy between the two adjacent molecules. Therefore, the energy exchange between two adjacent molecules will lead to the energy shift and splitting of absorption peaks ( Supplementary Fig. 12b). According to the measured absorption peak shift in Fig. 2g, the energy difference caused by polarized absorption can be calculated as: where λ90 and λ0 respectively refer to the wavelengths corresponding to 0° and 90° absorption peaks.
Meanwhile, the peak intensity can vary greatly in different polarization states. The polarization dependence of the Davydov components can be determined by the transition dipole moments (μ) from ground to excited states 13 . In a dimer system (two molecules in a crystal lattice), μ can be expressed as: where q is the elementary charge, r is the net distance of charge displacement,  and *  respectively represent the wavefunctions of ground and excited states, and the subscripts 1 and 2 refer to the two adjacent herringbone molecules (namely Molecule 1 and Molecule 2, respectively). The directions of μ in each molecule are marked by red arrows in Supplementary Fig. 12a according to the density function theory-calculated positions in Supplementary Table 4. For the transition from ground to the first excited state, the angle between μ and the molecular π plane is ~0.6°. Therefore, the arrangement of the in-plane projections of μ can be approximated to be the same as that of the herringbone-stacked C8-BTBT molecules. Consequently, we can label μ1 and μ2 respectively in two adjacent C8-BTBT molecules of a crystal lattice (Fig. 2f). By simple geometrical addition of vectors, we obtain the projections of μ along a axis (μa = μ2+μ1) and along b axis (μb = μ2-μ1). Since the absorption intensity can be described by the oscillator strength (f), which is proportional to the dipole strength (D = |μ| 2 ) (ref. 13 ). The anisotropic ratio of the peak intensity can be roughly estimated as 1/tan 2 (α/2) = 3.8 with a herringbone angle α of 54.2°. Note that due to the Davydov shift of the absorption peak, the absorption anisotropic ratio at a fixed wavelength can be larger (e.g., ~5.6 at 365 nm, Supplementary Fig. 13).   The absorption anisotropic ratio of C8-BTBT is calculated to be ~5.6 according to (AC8,max-

Supplementary
where AC8,max and AC8,min respectively represent the maximum and minimum absorbance of C8-BTBT, and Aquartz is the absorbance of the quartz substrate.

V. Calculations of the device performance
The hole mobility (μh) of the OPT in the saturation regime is calculated by: where L and the effective W are respectively 25 μm and 75 μm according to the device structure of the OPT ( Supplementary Fig. 14a-c). Ci is 1.2×10 -8 F cm -2 for a 300 nm-thick SiO2 layer 14 , and is ~1.8×10 -8 F cm -2 in our device configuration with ~200 nm-thick SiO2 serving as the gate dielectric. μh is calculated to be 2.6 cm 2 V -1 s -1 according to the slope of the black solid line in Supplementary Fig.   14d.
The figure-of-merit parameters of the OPT are calculated as follows. The photosensitivity is defined as the ratio of the photogenerated current (Iph) to the dark current (Idark). The responsivity (R) of a photodetector is: where Ilight is the drain current measured under light illumination, and P is the incident light power.
The noise equivalent power (NEP) is calculated by: where in is the noise density in A Hz -0.5 . The specific detectivity (D * ) of a photodetector is extracted according to: where A is the effective device area determined by 75×25 μm 2 in the channel region of the OPT, and Δf is the signal bandwidth.

VI. Characterizations of interfacial trap sites on SiO 2
To assess the critical role the SiO2/organic semiconductor interface played in charge trapping,  Fig. 18a,b), while the OPTs based on BCB and CYTOP dielectrics exhibit much inferior photoresponse ( Supplementary Fig. 18c,d). Since C8-BTBT was thermally deposited simultaneously on the above-mentioned dielectrics to exclude the possible device deviation caused by material growth, and the photoelectric measurements were conducted in a vacuum chamber to exclude the external influence of water/oxygen, we infer that the remaining interfacial active groups on SiO2 surface should be the main source of electron trap sites under illumination.
We further clarify the existence of electron trap sites on SiO2 by scanning kelvin probe force microscopy (SKPM, Asylum Research Cypher S). 50 nm-thick Au electrodes were thermally deposited on different gate dielectrics to function as the source/drain electrodes with heavily n-doped Si (n ++ Si) serving as the gate. SKPM measurements were conducted by scanning the channel between drain and source electrodes ( Supplementary Fig. 19a). During the scan, 10 V bias stress was applied at the gate while the source/drain electrodes were connected to ground, and the time-related potential change between the probe and the scanned surface was recorded. For SiO2 dielectric layer that is susceptible to interfacial active groups such as -OH, a positive gate bias voltage can induce an electrochemical change and lead to the trapping of negative charges ( Supplementary Fig. 19b). A possible mechanism can be expressed as 4-OH + O2 + 4e - 4-O -+ 2H2O in ambient air or 2-OH + 2e - 2-O -+ H2 when oxygen is not available 19 . The trapping of negative charges on SiO2 can be evidenced by the rapid potential drop with the increase of scanning time (left of Supplementary Fig. 19c). Further, zero gate bias voltage was applied after scanning the channel with 10 V bias stress for 255 s, a negative potential difference of ~-2.5 V can be observed in the channel region of SiO2 ( Supplementary Fig. 20a), indicating the strong capability of negative charge retention on SiO2 surface. In comparison, after passivating the SiO2 surface by active group-free CYTOP dielectric layer, the surface potential remains quite stable with negligible potential drop with increasing the scanning time (right of Supplementary   Fig. 19c), and the potential quickly recovers to 0 V upon applying zero bias stress ( Supplementary Fig.   20b), which confirms that the introduction of passivation layer can effectively eliminate the interfacial trap sites. water/oxygen can also lead to bias stress instability in OPTs (i.e., drift of transfer curves in the dark) 21 .

Supplementary
In order to acquire stable and repeatable photoresponse, we conducted all photoelectric measurements in vacuum unless otherwise mentioned.  represents for D* values that were estimated based on the dark current.

VIII. Theoretical estimation of partially polarized light detection
Conventionally, polarization navigation sensors require polarizers integrated with polarizationinsensitive photodetectors for the detection of partially polarized skylight. To evaluate their detection ability, we now consider a simplified case where the partially polarized incident light is composed of two orthogonally polarized parts, and the light intensities along these two directions are respectively denoted as Ipol, ‖ and Ipol, ⊥ . The degree of linear polarization (DoLP) of the incident light is thus (Ipol, ‖ -Ipol, ⊥ )/(Ipol, ‖ +Ipol, ⊥ ). For a linear polarizer, we define that the light transmittance along its optical axis is T ‖ , and perpendicular to the optical axis is T ⊥ , its extinction ratio (ER) is thus T ‖ /T ⊥ . If the partially polarized light passes through the polarizer ( Supplementary Fig. 37a In practical measurements, the DoLP of skylight is only about 60% (or even lower than 30% in UV spectral range) 48 , which results in Ipol, ‖ /Ipol, ⊥ of only ~4 (or ~1.9 in UV spectral range). Therefore, the increase of ER is favorable for more sensitive detection of partially polarized light ( Supplementary   Fig. 37b), while a small ER will lead to a degraded DR ( Supplementary Fig. 37c)

IX. Polarization navigation measurements
According to the single-scattering Rayleigh model 49 Fig. 39b,d). The normalized polarization-dependent IDS is fitted by: IDS(θ) = I ‖ cos 2 (θ+φ)+I ⊥ sin 2 (θ+φ) (S17) where I ‖ and I ⊥ respectively refer to the drain current along and perpendicular to the strongest photoresponse direction, θ is the angle with respect to the 0° reference direction, and φ is the angle between the 0° reference direction and the strongest photoresponse direction. The fitted strongest photoresponse directions are marked by red arrows in polar coordinates ( Supplementary Fig. 40a,c), which are ~-14° and ~-16° relative to the 0° reference direction (compass-pointed north), respectively.
We then look for the real-time solar azimuth angle (Φs) to determine the theoretical orientations of E  Fig. 5h,k, respectively. Therefore, Φs is in a range of 252° to 257° and 249° to 255°, respectively.
The theoretical orientations of E at zenith are thus -18° to -13° and -21° to -15° relative to the north (marked by red arrows in Supplementary Fig. 40b,d). Therefore, both the navigated directions of E (~-14° and ~-16° relative to the compass-pointed north) are located right in the range of the real-time theoretical values, indicating the high accuracy of our simplified celestial compass. More polarization navigation measurements at different times and in different weather conditions are presented in Supplementary Fig. 41 and Supplementary Table 7.